If I interpret your question correctly:

"Pick all rows where a has one of two given values, and b only exists in combination with one of them."

You can use any of the standard techniques laid out in the referenced answer.

• Select rows where value of second column is not present in first column

Just restrict your base table to the two given a. For instance

SELECT *
FROM   tbl t1
WHERE  a IN (1,2)
AND    NOT EXISTS (
   SELECT 1
   FROM   tbl t2
   WHERE  a IN (1,2)
   AND    t2.b =  t1.b
   AND    t2.a <> t1.a
   );

SQL Fiddle

This also works with duplicates on (a,b). Multiple identical rows would be returned.

If I interpret your question correctly:

"Pick all rows where a has one of two given values, and b only exists in combination with one of them."

You can use any of the standard techniques laid out in the referenced answer.

• Select rows where value of second column is not present in first column

Just restrict your base table to the two given a. For instance

SELECT *
FROM   tbl t1
WHERE  a IN (1,2)
AND    NOT EXISTS (
   SELECT 1
   FROM   tbl t2
   WHERE  a IN (1,2)
   AND    t2.b =  t1.b
   AND    t2.a <> t1.a
   );

SQL Fiddle

This also works with duplicates on (a,b). Multiple identical rows would be returned.